Page 77 - math 12

: ﺡﺮﻄﻟﺍﻭ ﻊﻤﺠﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﻟﺎﺘﻟﺍ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ
(2) ﻝﺎﺜﻣ
ّ
ِ
ِ
i) 3y -12 = 2y - |-30| ⇒ 3y-2y -12 = 2y- 2y- |-30|
⇒ y-12 +12 = -30+ 12 ⇒ y = -18
2
ii) 20 + 2h = 3h - 3 ⇒ 20 + 2h - 2h = 3h - 9 -2h
⇒ 20 + 9 = h -9 +9 ⇒ h = 29

iii) 2x + 2 3 = x- 3 3 ⇒ 2x + 2 3 - x = x- 3 3 –x ⇒ x + 2 3 = -3 3

⇒ x + 2 3 -2 3 = - 2 3 - 3 3 ⇒ x = -5 3

iv) |-3|m = 10 - −8 m ⇒ 3m = 10 + 2m ⇒ 3m -2m = 10 +2m – 2m ⇒ m = 10
3
ِﺔﻤﺴﻘﻟﺍﻭ ِﺏﺮﻀﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ [4-1-2]
ِ
ﱡ
Solving the Equations by using Multiplication and Division
َ
ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻤﺑ ﻰﻟﻭﻻﺍ ِﺔﺟﺭﺪﻟﺍ ِﺕﻻﺩﺎﻌﻣ ﻲﻓ ﺮﻴﻐﺘﻤﻟﺍ ﺔﻤﻴﻗ ﺩﺎﺠﻳﻹ ِﺔﻤﺴﻘﻟﺍﻭ ِﺏﺮﻀﻟﺍ ﻦﻴﺑ ﺔﻗﻼﻌﻟﺍ ﻞﻤﻌﺘﺳﺍ
ِ
ٍ
3 ﺎﻬﺴﻔﻨﻟ ْﺖﻈﻔﺘﺣﺎﻓ ،ﻦﻳﻮﻠﺗ ﻡﻼﻗﺍ ﺐﻠﻋ 5 ﻯﺮﺳ ْﺕﺮﺘﺷﺍ :ﻦﻳﻮﻠﺗ ﻡﻼﻗﺍ (3) ﻝﺎﺜﻣ
ُ
ﻥﺎﻜﻓ ﻱﻭﺎﺴﺘﻟﺎﺑ ﻊﺑﺭﻷﺍ ﺎﻬﺗﺍﻮﺧﺍ ﻰﻠﻋ ﻲﻗﺎﺒﻟﺍ ِﺖﻋﺯﻭﻭ ﺔﺒﻠﻋ ﻞﻛ ﻦﻣ ﻡﻼﻗﺍ
ﱢ
ُ
؟ ٍﺔﺒﻠﻋ ﻞﻛ ﻲﻓ ﻡﻼﻗﻷﺍ ُﺩﺪﻋ ﺎﻣ .ًﺎﻤﻠﻗ
؟ ٍﺔﺒﻠﻋ ﻞﻛ ﻲﻓ ﻡﻼﻗﻷﺍ ُﺩﺪﻋ ﺎﻣ .ًﺎﻤﻠﻗ 15 ﺎﻬﺗﺍﻮﺧﺍ ﻦﻣ ٍﺓﺪﺣﺍﻭ ﻞﻛ ﺔﺼﺣ
ِِ
ﱢ

n ﻮﻫ ﺔﺒﻠﻋ ﻞﻛ ﻲﻓ ﻡﻼﻗﻷﺍ ﺩﺪﻋ ﺽﺮﻓﺍ
5 ( n - 3) ÷ 4 = 15
ﻲﻫ ﺔﻟﺄﺴﻤﻟﺍ ﻞﺜﻤﺗ ﻲﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ ﺍﺬﻟ

5(n-3)

=15
4
5(n-3) 4 ﻲﻓ ﻑﺮﻁ ﻞﻛ ﺏﺮﺿﺃ
(4) = 15 (4)
4

5(n - 3) = 60 ﺱﻮﻘﻟﺍ ﻞﺧﺍﺩ ﻲﻓ 5 ﺏﺮﺿﺃ
ﻑﺮﻁ ﻞﻛ ﻰﻟﺍ + 15 ﻒﺿﺃ
5n -15 = 60

5n -15 +15 = 60 +15
5n = 75 5 ﻰﻠﻋ ﻑﺮﻁ ﻞﻛ ﻢﺴﻗﺃ
ﱢ
ِ
n = 15 ًﺎﻤﻠﻗ 15 ﻮﻫ ﺔﺒﻠﻋ ﻞﻛ ﻲﻓ ﻡﻼﻗﻷﺍ ُﺩﺪﻋ ﺍﺬﻟ
: ﺔﻟﺩﺎﻌﻤﻟﺎﺑ ﻞﺤﻟﺍ ﻦﻣ ﺎﻬﻴﻠﻋ ﺖﻠﺼﺣ ﻲﺘﻟﺍ (n=15 ) ﺮﻴﻐﺘﻤﻟﺍ ِﺔﻤﻴﻗ ﻦﻋ ﺽﻮﻋ : ُﻖّﻘﺤﺘﻟﺍ

ﱢ
ِ
5 (n- 3) ÷ 4 = 15
5 (15 - 3) ÷ 4 15
15 = 15
: ِﺔﻤﺴﻘﻟﺍﻭ ِﺏﺮﻀﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﻟﺎﺘﻟﺍ ﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ
ّ
(4) ﻝﺎﺜﻣ
i) x ÷ 12 = 4 ⇒ 4(12) = x ⇒ x = 4(12) ⇒ x = 48
6y 10 10 5
ii) 36 y ÷ 2 = |-5| ⇒ 6y÷ 2 = 5 ⇒ 6y = 10 ⇒ 6 = 6 ⇒ y = 6 ⇒ y = 3

76